Hooke’s Law is an equation that is named for Robert Hooke, a 17th century British physicist. Written F=-kx, it indicates that, within limits, the force required to stretch an elastic object, such as a spring, is directly proportional to the extension of the spring (x) modified by the spring constant for that spring. The negative sign in the equation indicates that the resulting force is restorative, pulling the spring back to its resting state. Hooke’s law generally holds for any situation where an elastic object is deformed by applied force, which creates applications for the law in seismology, acoustics, and spring-powered clocks.
By analyzing questions, you can see patterns emerge, patterns that will help you answer questions. Qwiz5 is all about those patterns. In each installment of Qwiz5, we take an answer line and look at its five most common clues. Here we explore five clues that will help you answer a tossup on Hooke’s Law.
SPRING While Hooke’s Law is generally demonstrated using a traditional metal-coil spring, a spring is really any object which deforms under force, but then, when the force is removed, returns to its previous shape. However, the spring will only do this to a certain point, after which it will cease to return to shape. This is known as the elastic limit of the spring.
Elasticity is the ability of an object to return to its original form after being stretched or compressed. Wire, in general, has this property--you could stretch a straight wire, and it would deform, then return to its original state, at least up to a point. A rubber ball or a diving board might be other examples. However, if the spring is extended or compressed beyond the elastic limit, it will no longer revert to the previous state. Deformation that goes beyond the elastic limit in this manner is known as plastic deformation.
Under Hooke’s Law, the restoring force is the force that acts to bring the spring back from an elastic state to a normal state. It acts in the opposite direction to the force that deformed the spring, and is responsible for creating the simple harmonic oscillation of the spring. Restoring force is the F in Hooke’s Law.
Thomas Young observed that objects of higher stiffness would resist elastic deformation. He defined that resistance as being a ratio E, calculated as the stress on the object (the applied force per unit area exerted) divided by the strain on said object (the amount of change in the length of the object over the original length). The resultant number is different for all materials. Young’s modulus is used to determine the spring constant k in Hooke’s Law.
SIMPLE HARMONIC OSCILLATOR
In an ideal system involving an absolute lack of friction, the original displacement of a mass would result in a restoring force which would compress the spring, resulting in a new restoring force in the opposite direction. Without friction, this motion would be a periodic function that is sinusoidal, or following a curve similar to a sine wave. A system of this sort is called a simple harmonic oscillator. However, in the real world, frictional forces will begin slowing the oscillation--this is called a damped harmonic oscillator.
Quizbowl is about learning, not rote memorization, so we encourage you to use this as a springboard for further reading rather than as an endpoint. Here are a few things to check out:
* Hooke was interested in a whole lot of things, not just springs. His observations made on various objects under the microscopes he designed became the basis of his book, Micrographia, which includes the very detailed image of a flea shown in this blog post by a visitor to the Royal Society.
* Robert Hooke and Isaac Newton were not fond of one another. The two clashed regularly, and you can read all the dirt about their ongoing battles here.
* If you’ve never heard of “Galloping Gertie” or the Tacoma Narrows Bridge, you should really take a look at this and learn why simple harmonic motion isn’t so simple in the real world.
* Confused by the descriptions above? Khan Academy has an easy-to-follow video to walk you through the concepts.
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